<h2>Problem 62</h2>
<div style="color:#666;font-size:80%;">30 January 2004</div><br />
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<p>The cube, 41063625 (345<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" />), can be permuted to produce two other cubes: 56623104 (384<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" />) and 66430125 (405<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" />). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.</p>
<p>Find the smallest cube for which exactly five permutations of its digits are cube.</p>

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